Neron-Severi group preserving lifting of K3 surfaces and applications

Abstract

For a K3 surface of finite height over a field of odd characteristic, there exists a smooth lifting to the ring of Witt vectors such that the reduction map from the Picard group of the generic fiber to the Picard group of the special fiber is isomorphic. In this paper, using this result, we give a criterion for a K3 surface of finite height over a field of odd characteristic to be an Enriques K3 surface or to be a K3 surface in terms of the Neron-Severi lattice. Then we show every Kummer surface has an Enriques involution. We also give a classification of K3 surfaces of Picard rank of 20 over odd characteristic.

References in corpus (1)

• Supersingular K3 Surfaces are Unirational

Cited by in corpus (8)

• Supersingular K3 Surfaces are Unirational
• On ordinary Enriques surfaces in positive characteristic
• The non-symplectic index of supersingular K3 surfaces
• On the number of Enriques quotients for supersingular K3 surfaces
• The moduli space of marked supersingular Enriques surfaces
• Existence of supersingular reduction for families of K3 surfaces with large Picard number in positive characteristic
• The representations of the automorphism groups and the Frobenius invariants of K3 surfaces
• Essential dimension of the moduli stack of polarized K3 surfaces